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Which of two powers is larger

Which is larger, 2¹⁰ or 10³? Ten 2s multiplied, against three 10s multiplied.

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2¹⁰ — ten 2s multiplied.
Step 1 of 4
  1. 2¹⁰ — ten 2s multiplied.
  2. 2¹⁰ = 1024.
  3. 10³ — three tens multiplied.
  4. 10³ = 1000. 2¹⁰ wins.

The rule

2¹⁰ is larger. It is 1024, and 10³ is 1000.

Same base above 1? The bigger count wins. Same count above 0? The bigger base wins. Neither the same? Work both out. With a base above 1, each extra copy makes the number bigger.

In the table, neither shortcut alone is right for every pair.

Four pairs, and what one shortcut alone would say
PairValuesLargerBigger base saysBigger count says
2¹⁰ and 10³1024, 10002¹⁰10³, wrong2¹⁰, right
3² and 2³9, 83²3², right2³, wrong
5³ and 3⁵125, 2433⁵5³, wrong3⁵, right
2⁴ and 4²16, 16tie4², wrong2⁴, wrong

Jump to lesson

This track

  1. 0 Start here
  2. 1 A short way to write a long multiplication
  3. 2 Two powers of one number, multiplied
  4. 3 Two powers of one number, divided
  5. 4 One power stacked on another
  6. 5 Walking the ladder down to zero
  7. 6 Every column is a power of ten
  8. 7 Writing a number too long to say
  9. 8 Which of two powers is larger
  10. 9 Counts below zero
  11. 10 Writing a very small number
  12. 11 Checkpoint: small powers and small numbers
  13. 12 The big picture
  14. 13 Track quiz

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